[PHK_seminar] [Cohomology]Wednesday 22 Apr, Pierre Bieliavsky

[Petr Somberg]

 This is our last moment reminder of our seminar!

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> Cohomology in algebra, geometry, physics and statistics
> Wednesday, 22 April 2026 - 13:30 to 14:30
> Place: Institute of Mathematics  of ASCR, Žitná 25, Praha 1, ZOOM  meeting
>
>
> Speaker: Pierre Bieliavsky, UCLouvain
> Title: Kinematical Lie algebras and symplectic symmetric spaces
> Abstract
>
>
> The notion of kinematical Lie algebra was introduced in physics for the
> classification of the various possible relativity algebras an isotropic
> spacetime can accommodate (H. Bacry and J. Levy-Leblond. Possible
> kinematics. J. Math. Phys., 9; 1968). Kinematical Lie algebras were
> classified in spacetime dimension four by brute force in the middle of
> the eighties. (H. Bacry and J. Nuyts. Classification of Ten-dimensional
> Kinematical Groups With Space Isotropy. J. Math. Phys., 27; 1986). More
> recently, those were reconsidered in a much wider context within the
> mathematical framework of Cartan geometry (José Figueroa-O'Farrill.
> Non-lorentzian spacetimes. Differ. Geom. Appl., 82; 2022).
>
>
> In a joint work with N. Boulanger (UMons), we recently gave an elementary
> proof of the fact that such a kinematical Lie algebra (and natural
> generalizations) always carries a canonical structure of symplectic
> involutive Lie algebra i.e. consists in the tangent version of a very
> specific class of symplectic symmetric spaces i.e. affine symmetric
> spaces equipped with parallel symplectic structures (Bieliavsky, P.,
> Boulanger, N.; Kinematical Lie algebras and symplectic symmetric spaces
> I. Lie algebraic aspects. Letters in Mathematical Physics, 116"(1),
> 2026). This geometrical result yields in particular an alternative
> classification of (generalized) kinematical Lie algebras of arbitrary
> dimension in purely symplectic geometric terms. It also establishes an
> unexpected strong relation between these spacetimes and contact
> sub-Riemannian symmetric spaces. In the talk, after having introduced the
> basic notions, I will explain these results. If time permits, I will show
> the implications within the currently fastly developing field of
> geometric actions.
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> We shall open ZOOM meeting at 13.15 for virtual coffee and close ZOOM at
> 15.30
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>
>
> Join Zoom Meeting
>
>
>
> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
>
>
>
> Meeting ID:99598413922
> Passcode:Galois
>
>
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>
>
> On Wednesday  April 29, Roee Leder  shall give     a talk on  Cohomology
> for linearized Ricci curvature
>
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> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
>
>
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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